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On a linear differential equation with a proportional delay

✍ Scribed by Jan Čermák

Publisher
John Wiley and Sons
Year
2007
Tongue
English
Weight
131 KB
Volume
280
Category
Article
ISSN
0025-584X

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✦ Synopsis

Abstract

This paper deals with the delay differential equation

We impose some growth conditions on c, under which we are able to give a precise description of the asymptotic properties of all solutions of this equation. Although we naturally have to distinguish the cases c eventually positive and c eventually negative, we show a certain resemblance between the asymptotic formulae corresponding to both cases. Moreover, using the transformation approach we generalize these results to the equation with a general form of a delay. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

📜 SIMILAR VOLUMES

Semigroups and Linear Partial Differenti
Semigroups and Linear Partial Differential Equations with Delay
✍ András Bátkai; Susanna Piazzera 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 145 KB

We prove the equivalence of the well-posedness of a partial differential equation with delay and an associated abstract Cauchy problem. This is used to derive sufficient conditions for well-posedness, exponential stability and norm continuity of the solutions. Applications to a reaction-diffusion eq